mac1147_lecture25_1_c

mac1147_lecture25_1_c - L25 Graphing General Sinusoidal...

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299 L25 Graphing General Sinusoidal Functions; Graphs of Other Trigonometric Functions General Sinusoidal Functions () sin sin yA x BA x B φ ωφ ω ⎛⎞ =− + = + ⎜⎟ ⎝⎠ , 0 ω> cos cos x x B + = + , 0 Amplitude: Period: Phase shift: Vertical shift: Steps in Graphing Sinusoidal Functions : 1. Determine the amplitude A and period 2 T π = . 2. Find the x -coordinate of the starting key point of one cycle , (phase shift), and the ending point, T + . 3. Divide the period T by 4: 4 T . 4. Find the x -coordinates of the other 3 key points: 4 T + , 44 TT + + , 444 TTT + ++ . 5. Find the y -coordinates of the five key points. 6. Plot the five key points in the coordinate system. 7. Fill in one cycle of the graph. 8. Continue the graph periodically to make it complete.
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300 Example : Graph: 3sin 2 1 3 yx π ⎛⎞ = −+ + ⎜⎟ ⎝⎠ .
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301 Example : Find the sinusoidal function ( ) sin yA x B ω φ = −+ from the graph given below. Note : Amplitude: maximum value - minimum value 2 A = Vertical shift: maxumum value + minimum value 2 B =
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302 Blood Pressure 8 100 20cos 5 P t π =−
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This note was uploaded on 11/07/2011 for the course MAC 1147 taught by Professor German during the Summer '08 term at University of Florida.

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mac1147_lecture25_1_c - L25 Graphing General Sinusoidal...

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